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Chapter 23: Problem 97

Carbon monoxide is toxic because it binds more strongly to the iron in hemoglobin (Hb) than does \(\mathrm{O}_{2}\), as indicated by these approximate standard free-energy changes in blood: $$ \begin{array}{ll} \mathrm{Hb}+\mathrm{O}_{2} \longrightarrow \mathrm{HbO}_{2} & \Delta G^{\circ}=-70 \mathrm{~kJ} \\\ \mathrm{Hb}+\mathrm{CO} \longrightarrow \mathrm{HbCO} & \Delta G^{\circ}=-80 \mathrm{~kJ} \end{array} $$ Using these data, estimate the equilibrium constant at \(298 \mathrm{~K}\) for the equilibrium $$ \mathrm{HbO}_{2}+\mathrm{CO} \rightleftharpoons \mathrm{HbCO}+\mathrm{O}_{2} $$

Short Answer

Expert verified
The equilibrium constant for the reaction \( \mathrm{HbO}_{2}+\mathrm{CO} \rightleftharpoons \mathrm{HbCO}+\mathrm{O}_{2} \) at 298 K is approximately 55.6.

Step by step solution

01

Manipulate the given reactions to obtain the reaction of interest

First, we need to rearrange the given reactions (1) and (2) to obtain the reaction we are looking for. We can achieve this by reversing reaction (1) and adding it to reaction (2): Reverse reaction (1): $$ \mathrm{HbO}_{2} \longrightarrow \mathrm{Hb}+\mathrm{O}_{2} \hspace{1cm} \Delta G^{\circ}_{1R}=70 \mathrm{~kJ} $$ Add reversed reaction (1) to reaction (2): $$ \mathrm{HbO}_{2}+\mathrm{CO} \rightleftharpoons \mathrm{HbCO}+\mathrm{O}_{2} \hspace{1cm} \Delta G^{\circ}=\Delta G^{\circ}_{1R}+\Delta G^{\circ}_2 $$
02

Calculate the standard free-energy change for the reaction of interest

Now we calculate the standard free-energy change for the reaction of interest by summing the standard free-energy changes of the manipulated reactions: $$ \Delta G^{\circ}=\Delta G^{\circ}_{1R}+\Delta G^{\circ}_2 = 70 \mathrm{~kJ} + (-80 \mathrm{~kJ}) = -10 \mathrm{~kJ} $$
03

Calculate the equilibrium constant at 298 K

We can calculate the equilibrium constant (K) using the following formula, relating the standard free-energy change to the equilibrium constant: $$ \Delta G^{\circ}=-RT\ln K $$ where R is the gas constant (8.314 J/mol·K) and T is the temperature in Kelvin (298 K). We can rearrange the formula to solve for K: $$ K=e^{-\frac{\Delta G^{\circ}}{RT}} $$ Plugging in the values: $$ K=e^{-\frac{-10\mathrm{~kJ/mol}}{(8.314 \times 10^{-3}\mathrm{~kJ/mol·K})(298\mathrm{~K})}} $$ $$ K\approx e^{4.02} \approx 55.6 $$ The equilibrium constant for the reaction at 298 K is approximately 55.6.

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Most popular questions from this chapter

A Cu electrode is immersed in a solution that is \(1.00 \mathrm{M}\) in \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) and \(1.00 \mathrm{M}\) in \(\mathrm{NH}_{3}\). When the cathode is a standard hydrogen electrode, the emf of the cell is found to be \(+0.08 \mathrm{~V}\). What is the formation constant for \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} ?\)

For each of the following metals, write the electronic configuration of the atom and its \(3+\) ion: (a) \(\mathrm{Ru},(\mathbf{b}) \mathrm{Mo},(\mathbf{c}) \mathrm{Co} .\) Draw the crystal-field energy-level diagram for the \(d\) orbitals of an octahedral complex, and show the placement of the \(d\) electrons for each \(3+\) ion, assuming a weak-field complex. How many unpaired electrons are there in each case?

Write out the ground-state electron configurations of (a) \(\mathrm{Ti}^{3+}\) (b) \(\mathrm{Ru}^{2+},(\mathrm{c}) \mathrm{Au}^{3+}\) (d) \(\mathrm{Mn}^{4+}\).

(a) What is the meaning of the term coordination number as it applies to metal complexes? (b) Give an example of a ligand that is neutral and one that is negatively charged. (c) Would you expect ligands that are positively charged to be common? Explain. (d) What type of chemical bonding is characteristic of coordination compounds? Illustrate with the compound \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{3}\) (e) What are the most common coordination numbers for metal complexes?

(a) A compound with formula \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) is dissolved in water, forming a solution that is approximately the same color as the solid. Immediately after forming the solution, the addition of excess \(\mathrm{AgNO}_{3}(a q)\) forms \(2 \mathrm{~mol}\) of solid \(\mathrm{AgCl}\) per mole of complex. Write the formula for the compound, showing which ligands are likely to be present in the coordination sphere. (b) After a solution of \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) has stood for about a year, addition of \(\mathrm{AgNO}_{3}(a q)\) precipitates \(3 \mathrm{~mol}\) of \(\mathrm{AgCl}\) per mole of complex. What has happened in the ensuing time?
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